Question

for the following questions you will need to create your own diagrams. draw them carefully and refer to the written description to ensure you find the correct solution.

1. the foot (bottom) of a ladder is placed 1.5 m from a wall. the ladder makes a 70° angle with the level ground. find the length of the ladder. (round to one decimal place.)

Explanation:

Step1: Identify the trigonometric relationship

We know the adjacent side (\(x = 1.5\) m) to the angle (\(\theta=70^{\circ}\)) and we need to find the hypotenuse (\(l\), length of the ladder). We use the cosine formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(l=\frac{x}{\cos\theta}\).

Step2: Substitute the values

Substitute \(x = 1.5\) m and \(\theta = 70^{\circ}\). We know that \(\cos70^{\circ}\approx0.3420\). Then \(l=\frac{1.5}{0.3420}\).

Step3: Calculate the value

\(l=\frac{1.5}{0.3420}\approx4.4\) m.

Answer:

The length of the ladder is approximately \(4.4\) m.